Program adaptation: To calculate inclusive backward proton cross sections

Computer Physics Communications 18 (1979) 155—162 © North-Holland Publishing Company

PROGRAM ADAPTATION: TO CALCULATE INCLUSIVE BACKWARD PROTON CROSS SECTIONS K.J.M. MORIARTY

*

Department of Physics, Technion — Israel Institute of Technology, Technion City, Haifa, Israel 32000

and H.N. THOMPSON Department of Mathematics, Royal Holloway College, Englefield Green, Egham, Surrey, TW2O 0EX, UK Received 4 December 1978

ADAPTATION SUMMARY

Additional keywords: backward single-particle-inclusive cross section, degenerate hypergeometric functions

Title of adaptation: BACKWARD INCLUSIVE PROTONS

Nature of physical problem This adaptation involves the phenomenological analysis and display (via printer and graph plotter) of high-energy back-

Adaptation number: 0001 Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland (see application form in this issue)

ward inclusive single-particle production cross sections. Method of solution The program be run under either the fixed t or the 2 modes forcan calculating differential cross sections. In fixed the M fixed t mode the t-bin is integrated over by 8-point Gaussian

Reference to original program: Cat. No.: AAUR; Title: ONCPLT; Ref in CPC: 12(1976) 277

quadrature. The results are plotted by using the graph plotting package APLOT and POLAR PLOT AND IMPROVEMENTS [1]. The program is compatible with the MINUIT minimization system [2].

Authors of original program: K.J.M. Moriarty and J.H. Tabor Computer: CDC 6600; Installation: University of London Computer Centre

Restrictions on the complexity of the program The number of inclusive cross section data points cannot exceed 500.

Number of bits in a word: 60 Number of cards required to effect adaptation: 401

Typical running time The test run took 42.8 s (of which 23.8 s was compilation time).

Card punching code: CDC CPC Library Cat. No. AAUN AAUN0001

*

subprograms used: Title APLOT POLAR PLOT AND IMPROVEMENTS

References [1] J. Anderson, K.J.M. Moriarty and R.C. Beckwith, Comput. Phys. Commun. 9 (1975) 85; J. Anderson, R.C. Beckwith, K.J.M. Moriarty and J.H. Tabor, Comput. Phys. Commun. 15 (1978) 437. [2] F. James and M. Roos, Comput. Phys. Commun. 10 (1975) 343.

Ref in CPC 9 (1975) 85 15 (1978) 437

Permanent address: Department of Mathematics, Royal Holloway College, Englefield Green, Egham, Surrey, TW2O OEX, UK. 155

KJ.M. Moriarty, ILN. Thompson / Backward inclusive protons

156

LONG WRITE-UP The original program ONCPLT [1] made provision calculating up to five different high-energy scattering processes. The matrix elements for the different processes are inserted in the TRACUI-—5 and/or TRACN1—5 subroutines. This adaptation demonstrates how this facility can be used for calculating a backward inclusive production process. The TRACU5 subroutine has been used in this case for the matrix element for the process x + p p + X. see fig. 1. In the configuration that is considered, a proton is produced fast forward after a pion beam has collided with a proton target. Thus the momentum transfer between initial state pion and final state proton is small. This momentum transfer is conventionally taken as u in backward scattering processes, but for simplicity of adaptation is taken as tin this program. The small momentum transfer in the ir -produced proton channel enables us to Reggeize and only ~ exchange is allowed. Further, the basic Regge-pole amplitudes are modified by the inclusion of absorption-type corrections. Details of the derivation of amplitudes can be found in ref. [21. Complex functions GINT and FINT are introduced to calculate sums over degenerate hypergeometric functions which arise in the absorption calculation. In the test run, the predictions are compared with data from CERN [3,4j. The Calcomp plotter output is shown in fig. 2. Clearly, the new subroutine can easily be modified to run without the absorption corrections or with di!’ferent absorption parameters. Additionally, by cliaiiging the couplings and external masses, the program could be used for the process K~+ p + X. for

:

—~

:

r

-*

Fig. I. The basic Regge-pole exchange diagram for the singleparticle-inclusive backward scattering process sr + p + X.

Fig. 2. Calcomp plotter output of the test run for the reaction ~ + P —~ p + X, with the results taken from the calculation ~t ref. 121 and the data taken from refs. [3,41.

157

Acknowledgements We wish to thank Professor H.G. Eggleston for encouragement in this work and J. Anderson for assistance in computing. We are grateful to Dr. R.W.B. Ardilh for his help in preparing this paper. One of us (H.N.T.) wishes to thank the S.R.C. for a Research Studentship.

References [1] K.J.M. Moriarty and J.H. Tabor, Comput. Phys. Commun. 12 (1976) 277. [2] K.J.M. Moriarty and H.N. Thompson, Phys. Rev. D2l (1980). [3] J. Six, Rapporteurs Talk, XIII Rencontre de Moriond [4] (1978). H. Yoshida, Ph.D. Thesis, Orsay (1977).

158

K.J.M. Moriarty, H.N. Thompson

/ Backward inclusive protons

TEST RUN OUTPUT

DATA SUPPL lED

P1—

+

PROTON

—

PROTON + X

PROCESS TYPE NO.

5

ThIS PROCESS IS BEAM FRAGNFNTATIQN,I.E. ,IFRAG ThE S—CHANNEL REGGEOM—PARTICLE SCATTERING AMI AN2 Ar-tI

= = =

.13500 GEV .93800 GEV .93800 GEV

SPIN FACTOR QUARK FACTOR

= =

1.00000 1.00000

VERTEX COUPLINGS POLE

G1

DELTA

G2

1.00000

1.00000

LABORATORY NUNENTUM

=

12.000000 GEV/C

LABORATORY ENERGY

=

12.000759 GE’v

=

23.41 1494 GEVISIII2

CEMTRE—OF—i-~SS ENERGY SQUARED SQUARE ROOT OF THE CENTRE—0F—N~SS ENERGY

=

4.838543 0EV

3-413r-ENTUM

=

2.325320 GEV/C

CENTRE—CF—N~SS ENERGY OF PARTICLE 1

=

2.330234 GEV

CENTRE—UF---r-~SS ENERGY OF PARTICLE 2

=

2.508306 GEV

U(5,6) COUPLING CONSTANT

=

1.000000

N3RF1~LIZ~RTI3N = ABSORPTION COEFFICIENTS

.000293

C

=

.700000

LAr-EDA

=

.068000

INITIAL STATE

GEVIIIIII (—4)

INCLUSIVE TOTAL CROSS—SECTION INTEGRAL LIMITS NWIII2/5 (~1~XI

=

.300000

GEVIIIIII2

(MININ1JM)

=

.000500

GEVIIIIII2

~piiIi2

T (NI~XINIJNI

=

T(MINIrIJF-Q

=

1 .800000 (0EV/C) 1i11i2 .000500

=

0

IS NOT EXOTIC,LE.

(GEV/C)i1ii1i2

,

IEXUTC

=

0

K.J.M. Moriarty, H.N. Thompson /Backward inclusive protons UPPER LIMIT (IF THE 4—t-13r~ENTUM TRANSFER T

=

.400000 (0EV/C) irir2

[email protected] LIMIT OF THE 4—tI3NENTUM TRANSFER T

=

.350000 (0EV/C) sara

r-~rz2

D2S —X———— P1 DTDNQ

ERROR

TMIN

.0739940 .0789250 .0826020 .0863930 .0881790 .1054050 .1109510 .1188700 .1271870 .1543030 .1562680 .1684290

.0041700 .0043070 .0044110 .0045060 .0045520 .0049770 .0051060 .0052650 .0054670 .0060220 .0060600 .0062910

.1602396 .1718447 .1837356 .1959236 .2084203 .2212384 .2343910 .2478921 .2617565 .2760000 .2906393 .3056921

S

4.20000 4.40000 4.60000 4.80000 5.00000 5.20000 5.10000 5.60000 5.80000 6.00000 6.20000 6.40000

UPPER LIMIT (IF THE 4—tl3F-EMTUM TRANSFER T

=

.550000 (GEV/Czir2

LOl-ER LIMIT oF THE 4-~ONENTUMTRANSFER T

=

.500000 (0EV/C)

r~Fx2

S

D25

—x—————

Tt-~X

17.3955334 17.1912890 16.9867587 16.7819315 16.5767953 16.3713379 16.1655460 15.9594055 15.7529017 15.5460189 15.3387403 15.1310481

9—FINAL

1.8522055 1.8290091 1.8057512 1.7624295 1.7590414 1.7355842 1.7120551 1.6884512 1.6647691 1.6410056 1.6171570 1.5932195

159

E3

2.0761766 2.0555092 2.0348418 2.0141745 1.9935071 1.9728397 1.9521723 1.9315049 1.9108376 1.8901702 1.8695028 1.8488354

E4

2.7623659 2.7830333 2.6037007 2.6243660 2.8450354 2.8657028 2.8863702 2.9070376 2.9277049 2.9483723 2.9690397 2.9897071

i1a1i2

ERROR

TMIN

.0036050 .0037120 .0037680 .0037620 .0044570 .0042420 .0046500 .0048450 .0050200 .0055570 .0053980 .0056070 .0063230 .0062920 .0065650 .0068180 .0072090 .0075610 .0074280 .0080200

.1602396 .1716447 .1837356 .1959236 .2084203 .2212384 .2343910 .2478921 .2617565 .2760000 .2906393 .3056921 .3211773 .3371153 .3535274 .3704367 .3879009 .4058969 .4243603 .4434248

TMAX

9—FINAL

E3

E4

Pr DTDrQ 4.20000 4.40000 4.60000 4.80000 5.00000 5.20000 5.40000 5.60000 5.60000 6.00000 6.20000 6.40000 6.60000 6.60000 7.00000 7.20000 7.40037 7.60054 7.79954 7.99854

.0553170 .0586300 .0604210 .0602120 .0845200 .0765750 .0920100 .0998800 .1072190 .1314260 .1240000 .1337860 .1701470 .1684460 .1834220 .1977810 .2211660 .2432880 .2347580 .2736830

17.3955334 17.1912690 16.9867587 16.7819315 16.5767953 16.3713379 16.1655460 15.9594055 15.7529017 15.5460189 15.3387403 15.1310481 14.9229235 14.7143462 14.5052948 14.2957461 14.0852831 13.8744858 13.6643484 13.4536100

1.8522055 1.8290091 1.6057512 1.7824295 1.7590414 1.7355842 1.7120551 1.6884512 1.6647691 1.6410056 1.6171570 1.5932195 1.5691891 1.5450614 1.5208317 1.4964952 1.4720008 1.4474134 1.4228466 1.3981506

2.0761766 2.0555092 2.0348418 2.0141745 1.9935071 1.9728397 1.9521723 1.9315049 1.9106376 1.8901702 1.8695028 1.8488354 1.8281660 1.8075007 1.7868333 1.7661659 1.7454600 1.7247752 1.7042114 1.6836476

2.7623659 2.7830333 2.8037007 2.6243680 2.8450354 2.8657028 2.8863702 2.9070376 2.9277049 2.9483723 2.9690397 2.9897071 3.0103745 3.0310418 3.0517092 3.0723766 3.0930825 3.1137673 3.1343311 3.1548949

160

K.J.M. Moriarty, H.N. Thompson /Backward inclusive protons

UPPER LIMIT OF THE 1—tI3NENTUM TRANSFER T

=

.700000 (0EV/C) IIIIr2

LOL.ER LIMIT OF THE 4-4i3NENTUM TRANSFER T

=

.650000 (0EV/C) IIIg2

NPes~2

S

4.20000 4.40000 4.60000 4.80000 5.00000 5.20000 5.40000 5.60000 5.80000 6.00000 6.20000 6.40000 6.60000 6.80000 7.00000 7.20000 7.40037 7.60054 7.79954 7.99654

D2S —X--—---— P1 DTDF2

ERROR

TMIN

.0409210 .0414160 .0449110 .0555890 .0608980 .0646130 .0592550 .0666550 .0748220 .0866260 .0935210 .1007960 .1130420 .1279480 .1383540 .1395820 .1602610 .1776180 .2038440 .2257390

.0031010 .0031200 .0032490 .0036440 .0037830 .0039030 .0037320 .0039580 .0041930 .0045120 .0046880 .0048670 .0051540 .0054630 .0057320 .0057290 .007740D .0064610 .0069210 .0072830

.1602396 .1718447 .1837356 .1959236 .2084203 .2212364 .2343910 .2478921 .2617565 .2760000 .2906393 .3056921 .3211773 .3371153 .3535274 .3704367 .3879009 .4058969 .4243603 .4434248

UPPER LIMIT OF THE 4—t13r-ENTUN TRANSFER T

=

.850000 (0EV/C) i1ii1i2

LOL.ER LIMIT OF THE 4-413r-ENTUM TRANSFER T

=

.800000 (0EV/C)

r.ccr2

S

D25

TN~~X

17.3955334 17.1912890 16.9867587 16.7819315 16.5767953 16.3713379 16.1655460 15.9594055 15.7529017 15.5460189 15.3387403 15.1310481 14.9229235 14.7143462 14.5052948 14.2957461 14.0852831 13.8744858 13.6643484 13.4636100

0—FINAL

1.8522055 1.8290091 1.8057512 1.7824295 1.7590414 1.7355842 1.7120551 1.6884512 1.6647691 1.6410055 1.6171570 1.5932195 1.5691891 1.5450614 1.5208317 1.4964952 1.4720008 1.4474134 1.4228465 1.3981506

E3

2.0761766 2.0555092 2.0348418 2.0141745 1.9935071 1.9728397 1.9521723 1.9315049 1.9108376 1.8901702 1.8695028 1.8488354 1.8281680 1.8075007 1.7868333 1.7661659 1.7454600 1.7247752 1.7042114 1.5836476

E4

2.7623659 2.7830333 2.8037007 2.8243680 2.8450354 2.8657028 2.8863702 2.9070376 2.9277049 2.9483723 2.9690397 2.9897071 3.0103745 3.0310418 3.0517092 3.0723766 3.0930825 3.1137673 3.1343311 3.1548949

~IiiIi2

ERROR

TMIN

.0024350 .0024460 .0030160 .0030430 .0032160 .0031670 .0033440 .0036910 .0036310 .0038730 .0041800 .0044030 .0047090 .0047610 .0052140 .0050920 .0056220 .0057530 .0060520 .0064910

.1602396 .1718447 .1837356 .1959236 .2084203 .2212364 .2343910 .2478921 .2617565 .2760000 .2906393 .3056921 .3211773 .3371153 .3535274 .3704367 .3879009 .4058969 .4243603 .4434248

TMAX

0—FINAL

E3

54

P1 DTD~Q 4.20000 4.40000 4.60000 4.80000 5.00000 5.20000 5.40000 5.60000 5.80000 6.00000 6.20000 6.40000 6.60000 6.80000 7.00000 7.20000 7.40037 7.60054 7.79954 7.99654

.0252230 .0254650 .0387190 .0393910 .0440250 .0426850 .0475830 .0579840 .0561020 .0638310 .0743490 .0825090 .0943200 .0964650 .1156490 .1103350 .1345050 .1408400 .1558450 .1792670

17.3955334 17.1912890 16.9867587 16.7819315 16.5767953 16.3713370 16.1655460 15.9594055 15.7529017 15.5460189 15.3387403 15.1310481 14.9229235 14.7143462 14.5052948 14.2957461 14.0852831 13.6744858 13.6643484 13.4536100

1.8522055 1.8290091 1.6057512 1.7824295 1.7590414 1.7355842 1.7120551 1.6884512 1.6647691 1.6410056 1.6171570 1.5932195 1.5691891 1.5450614 1.5208317 1.4964952 1.4720008 1.4474134 1.4228165 1.3981506

2.0761766 2.0555092 2.0348418 2.0141745 1.9935071 1.9728397 1.9521723 1.9315049 1.9108376 1.6901702 1.8695028 1.6468354 1.8281680 1.8075007 1.7868333 1.7661659 1.7464600 1.7247752 1.7042114 1.5836476

2.7623659 2.7830333 2.8037007 2.8243680 2.8450354 2.8657028 2.8863762 2.9070376 2.9277049 2.9483723 2.9690397 2.9897071 3.0103745 3.0310418 3.0517092 3.0723766 3.0030825 3.1137573 3.1343311 3.1546040

K.J.M. Moriarty, H.N. Thompson /Backward inclusive protons

161

Ilcinnar RESULTS I~U**

P1— + PROTON

—

PROTON + X

LABORATORY ~13r-ENTUM

=

UPPER LIMIT FOR THE 4—l~Or-EN11JM TRANSFER T

=

.400000

(6EV/C) ~2

LOI.ER LIMIT FOR THE 4—r-Or-NTUM TRANSFER T

=

.350000

(0EV/C) ~*2

r-c~z2

S D2S —x—-----— P1 DTDFQ

4.20000 4.40000 4.50000 4.80000 5.00000 5.20000 5.40000 5.60000 5.80000 6.00000 6.20000 6.40000

.07399400 .07692500 .08280200 .08639300 .08817900 .10540500 .11095100 .11667000 .12716700 .15430300 .15626800 .16842900

UPPER LIMIT FOR THE 4—4~O~ENTUMTRANSFER T LOI.ER LIMIT FOR THE 4-4~U?~ENTUM TRANSFER T

£1~X2

S

12.000000 6EV/C

ERROR

UNNATURAL

NATURAL

.00417000 .00430700 .00441100 .00450600 .00455200 .00497700 .00510600 .00528500 .00546700 .00602200 .00606000 .00629100

.08169868 .09049354 .09630702 .10214103 .10800936 .11394235 .11999289 .12627180 .13292644 .14023611 .14862584 .15881120

.00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000

TOTAL

.08169868 .09049354 .09630702 .10214103 .10800936 .11394235 .11999289 .12627180 .1329284.4 .14023611 .14662584 .15881120

CHISO

6.58985190 7.21452385 9.37381096 12.21434635 18.97826959 2.94246477 3.13586354 1.96148151 1.10291714 5.45650479 1.59032963 2.33728877

.550000 (6EV/C) ~2

=

D2S

.500000 (6EV/C) ~

ERROR

UNNATURAL

NATURAL

.00360500 .00371200 .00376800 .00376200 . 00445700 .00424200 .00465000 .00464500 .00502000 .00555700 .00539800 .00560700 .00632300 .00629200 .00656500 .00681800 .00720900 .00756100 .00742000 .00802000

.06629611 .07206332 .07793795 .08390039 .08990970 .09593669 .10194691 .10769530 .11375781 .11949232 .12507029 .13048602 .13571725 .14079092 .14579027 .15078861 .15602339 .16189517 .16901235 .17862087

.00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000

TOTAL

CHISQ

—x—-——— P1 DTDr-2 4.20000 4.40000 4.60000 4.60000 5.00000 5.20000 5.40000 5.60000 5.80000 6.00000 6.20000 6.40000 6.50000 6.80000 7.00000 7.20000 7.40037 7.60054 7.79954 7.99854

.05531700 .05863000 .06042100 .06021200 .08452000 .07657500 .09201000 .09986000 .10721900 .13142600 .12400000 .13378600 .17014700 .16844800 .18342200 .19778100 .22116600 .24326600 .23475800 .27368300

UPPER LIMIT FOR THE 4—rI3NENTUM TRANSFER T

=

.700000 (6EV/C) ir.z2

LOI=ER LIMIT FOR THE 4—t-Or-EN11JM TRANSFER T

=

.650000 (6EV/C) zsI2

.06629611 .07206332 .07793795 .08390039 . 08990970 .09593669 .10194691 .10789530 .11375761 .11949232 .12507029 .13048602 .13571725 .14079092 .14579027 .15078861 .15602339 .16189517 .16901235 .17862087

0.27520455 13.09635946 21.61200084 39.64911773 1.46232489 20.83312253 4.56664323 2.73685711 1.69563987 4.61176966 .03931311 .34638727 29.61977573 19.32124494 32.85783996 47.50518516 81.55451739 115.88143119 78.34121471 140.49677317

K.J.M. Moriarty, H.N. Thompson / Backward inclusive protons

162 t~P~2

S

D2S

ERROR

UNNATURAL

NATURAL

.00310100 .00312000 .00324900 .00364400 .00376300 .00390300 .00373200 .00395800 .00419300 .00451200 .00468800 .00466700 .00515400 .00548300 .00573200 .00572900 .00774000 .00646100 .00692100 .00728300

.04728866 .05243487 .05783027 .06346216 .06931006 .07536262 .08161008 .08797986 .09448486 .10104950 .10763367 .11416854 .12060509 .12688270 .13291440 .13862385 .14390988 .14867696 .15290862 .15657056

.00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000

TOTAL

Cl-USa

—x———— P1 DTD~’Q 4.20000 4.40000 4.60000 4.80000 5.00000 5.20000 5.40000 5.60000 5.80000 6.00000 6.20000 6.40000 6.60000 6.80000 7.00000 7.20000 7.40037 7.60054 7.79954 7.99854

.04092100 .04141600 .04491100 .05558900 .06089800 .06461300 .05925500 .06665500 .07462200 .08662600 .09352100 .10079600 .11304200 .12794600 .13835400 .13968200 .16026100 .17761800 .20384400 .22573900

UPPER LIMIT FOR THE 4—~rENTUMTRANSFER T

=

LOHER LIMIT FOR THE 4—4~O~NTUM TRANSFER T

~

S 025 —x————— P1 DTDr~2

4.20000 4.40000 4.60000 4.80000 5.00000 5.20000 5.40000 5.60000 5.80000 6.00000 6.20000 6.40000 6.60000 6.80000 7.00000 7.20000 7.40037 7.60054 7.79954 7.99854

.02522300 .02546500 .03871900 .03939100 .04402500 .04268500 .04758300 .05798400 .05610200 .06363100 .07434900 .08250900 .09432000 .09646500 .11564900 .11033500 .13450500 .14064000 .15584500 .17926700

NE TOTAL CROSS—SECTION AT

.04728866 .05243467 .05783027 .06346216 .06931006 .07536262 .08161008 .08797986 .09448486 .10104950 .10763367 .11416854 .12060509 .12688270 .132914-40 .13862385 .14390988 .14867696 .15290862 .15657056

4.21654612 12.47281968 15.81163749 4.66811531 4.94460537 7.30594429 35.88137192 29.02824399 21 .99093759 10.21887313 9.06239438 7.54927764 2.15332433 .03774923 .90057693 .03411405 4.46286050 20.Q6452021 54.16283434 90.19766706

.850000 (GEV/C) ~2 .800000 (0EV/C) ~2

ERROR

UNNATURAL

NATURAL

.00243500 .00244600 .00301600 .00304300 .00321600 .00316700 .00334400 .00369100 .00363100 .00387300 .00418000 .00440300 .00470900 .00476100 .00521400 .00509200 .00562200 .00575300 .00605200 .00649100

.02984200 .03371427 .03787515 .04233489 .04709575 .05216144 .05753002 .06320017 .06916392 .07541459 .08193422 .08869925 .09566425 .10281801 .11007600 .11738253 .12467245 .13182959 .13870060 .14522343

.00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000 .00000000

23.411494 GEV**2 IS

.050501786083 MILLE—BARNS

THE

.000000000000 MILLE—BARNS

THE TOTAL CHI—SQUARED AT THIS ENERGY

=

1183.51276585

THE TOTAL CHI—SQUARED FOR THIS PROCESS

=

1183.51276585

THE TOTAL CHI—SQUARED FOR THIS RUN

=

1183.51276585

THE NUF~EROF CALLS TO TCHISQ 15

1

.02984200 .03371427 .03787515 .04233469 .04709575 .05216144 .05753002 .06320017 .06916392 .07541459 .08193422 .08869925 .09566425 .10281801 .11007600 .11736253 .12467245 .13182959 .13870060 .14522343

.050501786083 NILLE—BARNS

THE UNNATURAL PARITY CONTRIBUTION 15 NATURAL PARITY CONTRIBUTION 15

TOTAL

CHISO

3.59830335 11.37413636 .07828311 .93592264 .91170057 8.95353497 8.64816762 1.99717369 12.94081662 8.94522355 3.29293777 1.97660100 .08146991 1.78058367 1.14244860 1.91556536 3.05879740 2.45301406 8.02502732 27.50724202